Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
168 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C72×Dic13 | C3 | semidirect |
| 3. C7×#11763957 | C3 | direct (N × H) |
| 4. C3×C7×#63270 | C4 | semidirect |
| 7. C3×#11763957 | C7 | direct (N × H) |
| 9. C72×Dic13 | C32 | semidirect |
| 10. C3×C72×C13 | C3×C4 | semidirect |
| 11. C7×#63270 | C3×C4 | semidirect |
| 17. C3×C7×Dic13 | ΓL(1,𝔽8) | semidirect |
| 18. C3×C7×Dic13 | C3×C7 | semidirect |
| 19. #11763957 | C3×C7 | direct (N × H) |
| 22. C3×#63270 | C4×C7 | semidirect |
| 24. C72×C13 | C32×C4 | semidirect |
| 35. C7×Dic13 | C3×ΓL(1,𝔽8) | semidirect |
| 36. C7×Dic13 | C32×C7 | semidirect |
| 40. C3×C7×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 41. C3×C7×C13 | C3×C4×C7 | semidirect |
| 42. #63270 | C3×C4×C7 | semidirect |
| 51. C3×Dic13 | C7×ΓL(1,𝔽8) | semidirect |
| 53. C3×C72 | Dic13⋊C3 | semidirect |
| 60. C7×C13 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 61. C7×C13 | C32×C4×C7 | semidirect |
| 71. Dic13 | C3×C7×ΓL(1,𝔽8) | semidirect |
| 72. C72 | C3×Dic13⋊C3 | semidirect |
| 78. C3×C13 | C4×C7×ΓL(1,𝔽8) | semidirect |
| 87. C3×C7 | C7×Dic13⋊C3 | semidirect |
| 88. C3×C7 | #11763957 | direct (N × H) |
| 94. C13 | C3×C4×C7×ΓL(1,𝔽8) | semidirect |
| 99. C7 | C3×C7×Dic13⋊C3 | semidirect |
| 100. C7 | C3×#11763957 | direct (N × H) |
| 105. C3 | C7×#11763957 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×#63270 | 2 |
| C3×C72×Dic13 | 3 |
| C7×#11763957 | 3 |
| C3×#11763957 | 7 |
| C3×C7×Dic13⋊C3 | 7 |
| C3×C4×C7×ΓL(1,𝔽8) | 13 |